theorem Th22:
  S is Sub_negative implies len @((Sub_the_argument_of(S))`1) < len @(S`1)
proof
  assume S is Sub_negative;
  then consider S9 such that
A1: S = Sub_not S9;
A2: 'not' (S9)`1 is negative;
  S`1 = 'not' (S9)`1 by A1;
  then
A3: len @the_argument_of ('not' (S9)`1) < len @(S`1) by A2,QC_LANG1:14;
  (Sub_the_argument_of(S))`1 = (S9)`1 by A1,Def30;
  hence thesis by A3,QC_LANG2:1;
end;
